In a rare coin collection, all coins are either pure gold or pure silv

Question

Tough and Tricky questions: Word Problems.

In a rare coin collection, all coins are either pure gold or pure silver, and there is initially one gold coin for every three silver coins. With the addition of 10 more gold coins to the collection, the ratio of gold coins to silver coins is 1 to 2. Based on this information, how many total coins are there now in this collection (after the acquisition)?

A) 40
B) 50
C) 60
D) 80
E) 90

Kudos for a correct  solution .

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manpreetsingh86 · Answer

no. of gold coins = x
no. of silver coins = y
thus, initially x/y =1/3 or y=3x -------------------1)
after addition of 10 gold coins, this ratio becomes 1/2, thus we have
 \frac{x+10}{y}  =  \frac{1}{2} 
2x+20=y , now from 1 we have
2x+20 = 3x
or x=20, also from from 1) y=3(20) =60
thus total number of coins after acquisition = 10+60+20 =90 hence E

intheend14 · Answer

Let's call g = # of gold coins and s = # of silver coins
Initially 3g = s and after the acquisition 2(g+10) = s
Let's solve the simultaneous equations by subtracting the second expression form the first expression: 3g-2g+20 = 0, yields g = 20.
After the acquisition we have 30 gold coins and double that in silver coins (60). A total of 90 coins.

Choice E

JJo · Answer

Let the no. of initial gold and silver coins be x & y resp.
Given, x/y = 1/3
y = 3x

Now, after adding 10 more gold coins, ratio is:
(x+10)/y = 1/2
2x+20 = y

substituting y,
2x+20 = 3x
x=20

hence, y=60

Total coins after addition of 10 gold coins: x+y+10 = 90

Ans. E

PareshGmat · Answer

Answer = E) 90

Gold ................... Silver .................. Total

x ........................ 3x .......................... 4x (Say "x" are initial gold coins)

x+10 .................. 3x ............................. 4x+10 (10 gold coins are added)

\frac{x+10}{3x} = \frac{1}{2}

x = 20

4x+10 = 90 = Total coins after addition

Bunuel · Answer

The correct answer is E.

DangerPenguin · Answer

I started with answer choice E. If the ratio is 1:2 after 10 gold coins are added and there are 90 total coins, there would be 30 gold coins and 60 silver coins. Before 10 were added, there were 20 gold coins and 60 silver coins which is 1:3.

Answer E!

Answer E!

Temurkhon · Answer

x - total number of coins before adding and gold is changing

(1/4)x+10=(1/3)*(x+10)

20/3=(1/12)*x

x=80, so after adding 80+10=90

if consider silver (not changing)

(3/4)x=(2/3)*(x+10)

(1/12)*x=20/3

x=80, 80+10=90

Can backsolve:

taking C (60) means that g/s=20/40 after adding, but before it should be 10/40 - not fit 1/3 (out) - should go more coins to fit ratio
taking D (80) means g/s is fractional, we need integer (number of coins), so out

E

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved by TESTing THE ANSWERS and some Number Properties.

I'm going to start with the last piece of information that we've been given: we're told that, at the end, the ratio of gold to silver coins is 1 to 2. This means that the TOTAL number of coins MUST be a multiple of 3...

eg.
1 gold and 2 silver = 3 total
2 gold and 4 silver = 6 total
3 gold and 6 silver = 9 total 
Etc.

From the Answers, there are only 2 numbers that are multiples of 3. Eliminate Answers A, B and D. From here, we can TEST either Answer C or Answer E - if it matches all of the given information, then it's the correct answer; if it does NOT match, then the OTHER answer is the correct answer.

Answer C: 60 coins

With 60 coins, at the end, we have that 1 to 2 ratio...

20 gold and 40 silver

We were told that ADDING 10 gold coins brought us to THAT ratio, so we can subtract those 10 gold coins away... We are now left with...

10 gold and 40 silver

At the beginning, we were told that we had 1 gold coin for ever 3 silver coins. However, here we have 1 gold coin for every 4 silver coins. This does NOT match what we were told, so this CANNOT be the answer. There's only one answer left...

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

KarishmaB · Answer

Another method is to note that final ratio of gold to silver coins is 1:2. So total coins will definitely be a multiple of (1+2) = 3. Only options (C) and (E) satisfy.

Now, initially, the total number of coins were in the ratio 1:3. So initial number of coins must be divisible by 4. 
(60 - 10) = 50 is not divisible by 4.
(90 - 10) = 80 is divisible by 4. This must be the answer 
Answer (E)

or to pick one of (C) and (E), you can check either.
If you pick (C), you know that final number of gold and silver coins must be 20 and 40. Then the number of gold coins must have been 10 before. That is a ratio of 1:4. But this is incorrect so answer must be (E).

hatemnag · Answer

traditional approach : 1x+10/3x = 1/2
3x = 2x + 20
x = 20
so Total # of coins in the collection = 30 gold + 60 silver = 90 coins

bumpbot · Answer

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In a rare coin collection, all coins are either pure gold or pure silv

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